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-A new method for the analytical evaluation of Richardson equations in the thermodynamical limit. We introduce a probability of the system of charges to occupy certain states in a configurational space and a partition function (Coulomb integral), from which energy can be found. -For the model with constant density of states, we calculated a ground state energy, which is given by a single expression all over from the dilute to dense regime of pairs. -The method is rather generic and can be applied to other pairing Hamiltonians, which have an electrostatic analogy (Bethe anzats?). -Rich math structure as well as numerous links with other topics of modern theoretical physics Summary